I found this rather interesting

suppose that a sequence [tex]{x_{n}}[/tex] satisfies

[tex] |x_{n+1}-x_{n}|<\frac{1}{n+1}[/tex] [tex] \forall n\epsilon N[/tex]

how couldnt the sequence [tex]{x_{n}}[/tex] not be cauchy? I tried to think of some examples to disprove it but i didnt achieve anything doing that, please help

thanxs